When a surgeon is to operate inside the eye of a patient, the presently used technique generally includes the insertion of a needle which provides for a supply of irrigation fluid as well as a passage for aspiration so that unwanted fluids and some solid matter can be aspirated from the eye. There are times when some tissue needs to be severed, and some prior art handpieces have been provided with cutting means in conjunction with the aspiration. The above identified co-pending application provides control circuitry whereby a pulsing pressure is provided to assist in cutting, but there are still times when the tissue is somewhat difficult to cut. Also, when aspiration is used within the eye, it sometimes happens that a piece of tissue inadvertently lodges within the aspiration port. If this tissue is not to be severed, it is sometimes quite difficult to remove the tissue from the aspiration port quickly and without causing trauma.